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h3. Definitions of Position and Velocity    [!copyright and waiver^SectionEdit.png!|Motion -- 1-D General (Definitions)]

If we start knowing the position vs. time {*}x ( t ){*}, then the velocity, {*}v ( t ){*}, is the derivative of its position, and the derivative in turn of this velocity is the particle's acceleration, {*}a ( t ){*}. The force is the particle's mass times {*}a ( t ){*}.
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{latex}\begin{large}\[ v = \frac{dx}{dt} \]\end{large}{latex}
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{latex}\begin{large}\[ a = \frac{dv}{dt} = \frac{d^{2}x}{dt^{2}}\]\end{large}{latex}
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In fact, as you can see, the velocity and acceleration are defined as derivatives of the position, a fact acknowledged by the phrase "the calculus of motion".  Newton had to invent calculus of one variable to deal with motion\!